John Neville Keynes e a silogística com termos negativos

Abstract

This work presents and discusses the extension of traditional Aristotelian syllogistics carried out by John Neville Keynes in the beginning of the twentieth century, through the introduction of a notation for negative terms into logical theory. The primary bibliography used was the fourth edition, dated 1906, of the Keynes‟s textbook on Logic Studies and Exercises in Formal Logic . Keynes has an extensional interpretation of the use of negative terms: they are understood as an extensional complement of the corresponding positive terms relative the universe of discourse; in this sense, his conception of the negation of terms obeys the Principle of Excluded Middle. The extension of traditional syllogistics by the addition of negative terms also leads to an extension of the number logical relations among the categorical propositions, as well as the number of valid immediate inferences. The Square of Oppositions is transformed into an Octagon of Oppositions, to which three new logical relations between the categorical propositions are added, namely, complementarity, sub-complementarity and contra-complementarity; the validity of these new logical relations does not require existential presupposition of any of the involved terms. Regarding immediate inferences, besides the conversion process, three new types of formal processes are obtained: obversion, contraposition (partial and total) and inversion (partial and total). To prove the validity of these formal processes, as well as of any syllogistic inference, Keynes lays out a diagrammatic method based on the well-known Euler method; in Keynes‟s method, however, negative terms are represented. In Keynes‟s version of Euler‟s diagrammatic method validity is understood as preservation of information: a collection of basic diagrams, corresponding to elementary information, is assigned to categorical propositions; and an inference is valid if, and only if, the diagrams assigned to the premises are also assigned to the conclusion.